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MHT CET202615 April 2026Evening ShiftMathematicsStraight LinesActual

The equation of the line passing through the point of intersection of the lines x + 2y + 6 = 0 and 2x - y = 2 and making an intercept 5 on the y-axis is

Options

  1. A39x + 2y - 10 = 0
  2. B39x - 2y + 10 = 0
  3. Cx + 4y - 20 = 0
  4. Dx - 4y + 20 = 0

Correct answer

B. 39x - 2y + 10 = 0

Step-by-step solution

Solving the given equations x + 2y + 6 = 0 and 2x - y = 2 . Multiplying the second equation by 2 and adding to the first gives 5x + 2 = 0 x = - 2 5 . Substituting x in the second equation gives y = 2 (- 2 5 ) - 2 = - 14 5 . The point of intersection is (- 2 5 , - 14 5 ) . The required line makes an intercept of 5 on the y-axis, so it passes through (0, 5) . The slope of the line is m = 5 - (- 14 5 ) 0 - (- 2 5 ) = 39 5 2 5 = 39 2 . The equation of the line is y = mx + c y = 39 2 x + 5 . Rearranging the terms gives

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